Identifying Proportional Relationships
When trying to identify whether or not a relationship between variables is proportional, which of the following steps can I take?
a. I can arrange the values given in a table into a pretty picture
b. I can multiply all of the numbers on the table by something
c. I can arrange all of the pairs of values as fractions and simplify the fractions to see if they are equal
c. I can arrange all of the pairs of values as fractions and simplify the fractions to see if they are equal
What word is missing at the beginning of this template that helps us describe ratio relationships?
????? x is _______ by ____, y is ________ by _____.
a. For
b. As
c. What
d. Breakthrough
b. As
There are 6 cookies for $12. How much does 1 cookie cost?
The cost is $2.00 per cookie.
-6 + 4 = ?
-2
What does the D stand for in PEMDAS?
D for Division!
If I simplify all the fractions I arrange from a table of values that represent two variables, and the simplified fractions are exactly the same, then I know that the relationship between the variables is NOT proportional. TRUE or FALSE?
FALSE - equal simplified fractions show that the relationship IS proportional!
What is the missing value in the table? See Slide 4
6
Sally has driving lessons. She drives 139 miles per hour. How many miles per minute does she drive? (Hint: there are 60 minutes in 1 hour)
Sally drives 2.32 miles per minute.
(-2) + (-8) = ?
-10
3 + (7 x 3) - 6 = ?
18
Is this relationship proportional? See Slide 2
YES!
Describe the relationship shown in the table (look for patterns for each variable, then use the template we learned about for writing descriptions) See Slide 5
As x is increasing by 3, y is increasing by 1.
Sally bought 2 basketballs for $10.00 and Bob bought 4 basketballs for $12.30. Who got the better deal?
Sally’s basketballs cost $5.00 per ball. Bob’s basketball’s cost $3.08 per ball. Bob got the better deal!
13
12 - 3 x 3 + (20 / 4) = ?
8
Is this relationship proportional? See Slide 3
No!
Describe the relationship shown in the table using words. See Slide 6
As x is being divided by 4, y is being divided by 3.
You can buy 5 ice creams for $12.24 from Store A and 8 ice creams for $15.57 from Store B. Which is the better deal?
Store A: The cost per ice cream cone is $2.45.
Store B: The cost per ice cream cone is $1.95.
Store B has the better deal.
In a football game, the first team started at the 3 yard-line and gained 3 more yards but then lost 10. Where is the team now?
3 + 3 + (-10) = -4. The team is now at the -4 yard-line
6 x (36 / 6) - 42 = ?
-6
In a weird alternate universe, for every 3 days of sunlight, 4 days of rain follow. Which of the following would also be true of this alternate universe?
a. There are 6 days of sunlight followed by 8 days of rain.
b. There are 6 days of sunlight followed by 12 days of rain.
c. There are 9 days of sunlight followed by 8 days of rain.
a. There are 6 days of sunlight followed by 8 days of rain.
Sky is baking cookies, and the ingredients are 4 cups of peanut butter to 5 cups of chocolate chips. Fill in the table, showing the relationship between cups of peanut butter and cups of chocolate chips. (See Slide 7)
See Slide 8
A man went skydiving, starting from 700 feet in the air. He dove down 45 feet in 1 minute. How many feet did he fall per second?
He fell 0.75 feet per second.
My friend let me borrow $5, and I didn’t have the money to pay her back. However, my mom then gave me $7 for good grades. Now that I can pay my friend back, how much money am I going to have left?
-5 + 7 = 2
I am going to have $2 left.
Mario bought a toy for $20, then 2 cans of dog food for $1 each and a bag of cereal for $3. When he paid, he used a $5 discount coupon. How much money did Mario spend?
20 + (2 x 1) + 3 - 5
Mario spent $20.